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Compactification of M Theory and Manifolds with G2 Holonomy

M 理论和流形的 G2 Holonomy 紧化

基本信息

批准号：
15540253
负责人：
EGUCHI Tohru
金额：
$ 2.18万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2006
项目状态：
已结题

项目摘要

In paper 2 we have applied the method of geometrical transition and computed the partition function of topological string theory on various non-compact Calabi-Yau manifolds using the link invariants of Chern-Simons theory. We have shown that the results of computation agree exactly with the formula proposed by Nekrasov for the N=2 supersymmetric gauge theory. And thus they establish the relation between topological string and N=2 SUSY gauge theory.In paper 3 we have used the representation theory of N=2 supersonformal algebra and the method of modular bootstrap and derived the boundary states of N=2 Liouville theory. N=2 Liouville theory is known to be T-dual to the coset SL(2;R)/U(1) model and our results on boundary states agree well with those known in SL(2;R)/U(1) theory.In paper 7 we have used the formula of Ashoke-Douglas for the distribution of flux vacua in type IIB string theory and evaluated the distribution function of flux vacua on the moduli space of Calabi-Yau manifolds. We have shown that the distribution function is peaked around the singular points in Calabi-Yau moduli space and have the universal behavior 1/(z^2 log z^2). Thus it diverges at the singular point z=0, however, it is still integrable around z=0 and there exist only a finite number of vacua around each Calabi-Yau singularity..In paper 8 we have studied the geometry of non-compact Calabi-Yau manifolds like ALE spaces and have proposed formula for their. elliptic genera based on the analysis of the representation theory of N=2,4 superconformal algebras. Our formula agrees with the one suggested from the decompactification of K3 surface by means of some non-trivial theta function identity.

在文献2中，我们应用几何变换的方法，利用Chern-Simons理论的链不变量计算了拓扑弦理论在各种非紧Calabi-Yau流形上的配分函数。计算结果与Nekrasov对N=2超对称规范理论提出的公式完全一致。在文3中，我们利用N= 2超形式代数的表示理论和模Bootstrap方法，导出了N=2 Liouville理论的边界态。N=2的Liouville理论是陪集SL（2;R）/U（1）模型的T-对偶，我们关于边界态的结果与SL（2;R）/U（1）理论的结果一致.在文7中，我们利用Ashoke-Douglas关于IIB型弦理论中通量真空分布的公式，计算了Calabi-Yau流形模空间上通量真空的分布函数.我们已经证明了分布函数在Calabi-Yau模空间中的奇点附近是峰值的，并且具有1/（z^2 log z^2）的普适行为。因此，它在奇点z=0处发散，然而，它在z=0附近仍然是可积的，并且在每个卡-丘奇点周围只存在有限个真空。在文8中，我们研究了类似ALE空间的非紧Calabi-Yau流形的几何，并给出了它们的公式。在分析N= 2，4超共形代数的表示理论的基础上，给出了N= 2，4超共形代数的一个新的椭圆形属.我们的公式与K_3曲面通过非平凡的θ函数恒等式解压缩所得到的公式一致。